You can fly on SQ and accrue your miles on UA's programme for example, but if the subload classes that Krisflyer don't give you the miles, then United's Mielage Plus won't give it to you either.

It is worthwhile noting that Krisflyer has some partners that other Star Alliance partners cannot offer like having Virgin and Delta Airlines as partners, as well as the ability to transfer miles from credit card partners which are Asian based.

If you don't live in this region - you are not forced to join. You do have a choice. However, if you fly on Cathay Pacific and the booking code is in W, you won't be able to accrue mileage on AAdvantage if you're a US member (Canadian members can accrue miles on fares as AsiaMiles members can).